Space of modular forms of level 1014, weight 3, and Character 1014.f

• Label: 1014.3.f
• Level: $1014$
• Weight: $3$
• Character orbit: 1014.f
• Rep. character: $\chi_{1014}(577,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $100$
• Newform subspaces: $12$
• Sturm bound: $546$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1014.f (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 12 \)
Sturm bound:			\(546\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1014, [\chi])\).

	Total	New	Old
Modular forms	784	100	684
Cusp forms	672	100	572
Eisenstein series	112	0	112

Trace form

100 * q + 4 * q^2 - 12 * q^5 - 8 * q^8 + 300 * q^9 - 24 * q^11 + 32 * q^14 + 24 * q^15 - 400 * q^16 + 12 * q^18 + 24 * q^20 - 24 * q^21 + 96 * q^22 + 112 * q^29 + 48 * q^31 - 16 * q^32 - 72 * q^33 - 72 * q^34 - 64 * q^35 + 84 * q^37 + 48 * q^40 - 132 * q^41 - 48 * q^44 - 36 * q^45 + 216 * q^47 - 164 * q^50 - 424 * q^53 - 208 * q^55 + 72 * q^57 - 240 * q^58 + 72 * q^59 - 48 * q^60 - 184 * q^61 + 192 * q^66 + 144 * q^67 - 112 * q^68 + 48 * q^70 + 408 * q^71 - 24 * q^72 + 36 * q^73 + 104 * q^74 + 128 * q^79 + 48 * q^80 + 900 * q^81 - 72 * q^83 - 48 * q^84 - 216 * q^85 + 48 * q^86 - 48 * q^87 + 156 * q^89 - 160 * q^92 + 168 * q^93 + 224 * q^94 - 60 * q^97 + 508 * q^98 - 72 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(1014, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1014.3.f.a	$1014$	$3$	1014.f	13.d	$4$	$4$	$2$	$27.629$	\(\Q(\zeta_{12})\)	None					78.3.f.a	$2$	$0$	\(-4\)	\(0\)	\(-12\)	\(4\)	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(\beta_1-1)q^{2}+\beta_{3} q^{3}-2\beta_1 q^{4}+\cdots\)
1014.3.f.b	$1014$	$3$	1014.f	13.d	$4$	$4$	$2$	$27.629$	\(\Q(\zeta_{12})\)	None					78.3.l.b	$2$	$0$	\(-4\)	\(0\)	\(6\)	\(8\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+(\beta_{2}-1)q^{2}+(-\beta_{3}+\beta_{2}-\beta_1)q^{3}+\cdots\)
1014.3.f.c	$1014$	$3$	1014.f	13.d	$4$	$4$	$2$	$27.629$	\(\Q(\zeta_{12})\)	None		✓			1014.3.f.c	$2$	$0$	\(-4\)	\(0\)	\(8\)	\(-4\)	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-\beta_1-1)q^{2}-\beta_{3} q^{3}+2\beta_1 q^{4}+\cdots\)
1014.3.f.d	$1014$	$3$	1014.f	13.d	$4$	$4$	$2$	$27.629$	\(\Q(\zeta_{12})\)	None					78.3.l.a	$2$	$0$	\(-4\)	\(0\)	\(12\)	\(10\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+(\beta_{2}-1)q^{2}+(\beta_{3}-\beta_{2}+\beta_1)q^{3}+\cdots\)
1014.3.f.e	$1014$	$3$	1014.f	13.d	$4$	$4$	$2$	$27.629$	\(\Q(\zeta_{12})\)	None					78.3.l.a	$2$	$0$	\(4\)	\(0\)	\(-12\)	\(-10\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-\beta_{2}+1)q^{2}+(\beta_{3}-\beta_{2}+\beta_1)q^{3}+\cdots\)
1014.3.f.f	$1014$	$3$	1014.f	13.d	$4$	$4$	$2$	$27.629$	\(\Q(\zeta_{12})\)	None		✓			1014.3.f.c	$2$	$0$	\(4\)	\(0\)	\(-8\)	\(4\)	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-\beta_1+1)q^{2}-\beta_{3} q^{3}-2\beta_1 q^{4}+\cdots\)
1014.3.f.g	$1014$	$3$	1014.f	13.d	$4$	$4$	$2$	$27.629$	\(\Q(\zeta_{12})\)	None					78.3.l.b	$2$	$0$	\(4\)	\(0\)	\(-6\)	\(-8\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-\beta_{2}+1)q^{2}+(-\beta_{3}+\beta_{2}-\beta_1)q^{3}+\cdots\)
1014.3.f.h	$1014$	$3$	1014.f	13.d	$4$	$8$	$4$	$27.629$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None					78.3.l.c	$2$	$0$	\(-8\)	\(0\)	\(-6\)	\(-2\)	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1-\beta _{2})q^{2}+(-\beta _{3}+\beta _{6})q^{3}+2\beta _{2}q^{4}+\cdots\)
1014.3.f.i	$1014$	$3$	1014.f	13.d	$4$	$8$	$4$	$27.629$	8.0.\(\cdots\).1	None					78.3.f.b	$2$	$0$	\(8\)	\(0\)	\(0\)	\(-4\)	$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1-\beta _{6})q^{2}+\beta _{1}q^{3}-2\beta _{6}q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
1014.3.f.j	$1014$	$3$	1014.f	13.d	$4$	$8$	$4$	$27.629$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None					78.3.l.c	$2$	$0$	\(8\)	\(0\)	\(6\)	\(2\)	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1+\beta _{2})q^{2}+(-\beta _{3}+\beta _{6})q^{3}+2\beta _{2}q^{4}+\cdots\)
1014.3.f.k	$1014$	$3$	1014.f	13.d	$4$	$24$	$12$	$27.629$		None		✓			1014.3.f.k	$2$	$0$	\(-24\)	\(0\)	\(-8\)	\(-24\)		$\mathrm{SU}(2)[C_{4}]$
1014.3.f.l	$1014$	$3$	1014.f	13.d	$4$	$24$	$12$	$27.629$		None		✓			1014.3.f.k	$2$	$0$	\(24\)	\(0\)	\(8\)	\(24\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{3}^{\mathrm{old}}(1014, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1014, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(338, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(507, [\chi])\)\(^{\oplus 2}\)